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Title: Spatial correlations in driven-dissipative photonic lattices

Abstract

In this paper, we study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array ($$\sim 1/z$$) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. ETH Zurich, Zurich (Switzerland)
  2. Princeton Univ., Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1500093
Grant/Contract Number:  
SC0016011
Resource Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 19; Journal Issue: 12; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum simulations; cavity arrays; cavity QED; circuit QED; many-body physics with photons

Citation Formats

Biondi, Matteo, Lienhard, Saskia, Blatter, Gianni, Türeci, Hakan E., and Schmidt, Sebastian. Spatial correlations in driven-dissipative photonic lattices. United States: N. p., 2017. Web. doi:10.1088/1367-2630/aa99b2.
Biondi, Matteo, Lienhard, Saskia, Blatter, Gianni, Türeci, Hakan E., & Schmidt, Sebastian. Spatial correlations in driven-dissipative photonic lattices. United States. doi:10.1088/1367-2630/aa99b2.
Biondi, Matteo, Lienhard, Saskia, Blatter, Gianni, Türeci, Hakan E., and Schmidt, Sebastian. Fri . "Spatial correlations in driven-dissipative photonic lattices". United States. doi:10.1088/1367-2630/aa99b2. https://www.osti.gov/servlets/purl/1500093.
@article{osti_1500093,
title = {Spatial correlations in driven-dissipative photonic lattices},
author = {Biondi, Matteo and Lienhard, Saskia and Blatter, Gianni and Türeci, Hakan E. and Schmidt, Sebastian},
abstractNote = {In this paper, we study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array ($\sim 1/z$) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.},
doi = {10.1088/1367-2630/aa99b2},
journal = {New Journal of Physics},
number = 12,
volume = 19,
place = {United States},
year = {2017},
month = {12}
}

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Cited by: 4 works
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Figures / Tables:

Figure 1 Figure 1: (a)Illustration of the self-consistent scheme explained in detail in the text in order to solve the equation of motion system. The solid blue (thin red) arrows indicate the procedure to obtain a lattice density matrix correct to second, 2nd (first,1st) order in 1/z. (b)Scaling of the dimension ofmore » the Liouvillian operator M2 × M2 with the number of lattice sites N, for the 1/z expansion (curves) and exact diagonalization (ED, symbols) for a system with maximally one particle per site np – 1. The scaling for larger np is similar.« less

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    Works referencing / citing this record:

    Multistability of Driven-Dissipative Quantum Spins
    journal, January 2020


    Quantum stabilization of photonic spatial correlations
    journal, December 2018


    Spectral theory of Liouvillians for dissipative phase transitions
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